The crime in question was the killing of Michael J. Sandy, 29, a gay man who was lured to a parking area in Sheepshead Bay last October, beaten and chased into traffic. He later died in the hospital.

Prosecutors have said a group of young men contacted Mr. Sandy through an online gay chat room, selecting him as a robbery victim in the belief that a gay man would be unwilling or unable to put up a fight and unlikely to report the crime.

The defendants -- John Fox, 20; Ilya Shurov, 21; and Anthony Fortunato, 21 -- have been charged not just with murder, but with murder under the state Hate Crimes Act of 2000, which provides longer prison sentences for crimes motivated ''in whole or in substantial part because of a belief or perception regarding the race, color, national origin, ancestry, gender, religion, religious practice, age, disability or sexual orientation of a person.''

Prosecutors and defense lawyers have presented contrasting interpretations of that phrase, the words it includes and the words it omits.

In court documents, a defense lawyer has asked Justice Konviser-Levine to dismiss the enhanced murder charges against all three defendants because ''the crimes alleged are not crimes of hate but rather crimes of opportunity.''

That lawyer, Gerald J. Di Chiara, filed a motion in which he argued that lawmakers responsible for the Hate Crimes Act had written a statute applicable only to defendants who truly hate their victims. He quoted from a State Senate memorandum in support of a law ''designed to ensure that only those who truly are motivated by invidious hatred are prosecuted for committing hate crimes.''

To allow prosecutors to pursue hate crime charges without demonstrating such hatred, Mr. Di Chiara argued, would render the law unconstitutionally vague and arbitrary.

For example, he wrote, the authorities could then ascribe hate crimes to ''a mugger who selects an elderly or disabled person because he believes that such a victim will be unable to resist effectively, a pocketbook snatcher who targets women, or a burglar who selects a victim from an ethnic minority group because the victim does not speak English.''

In response, prosecutors filed a response drafted by Seth M. Lieberman, senior appellate counsel to the Brooklyn district attorney. Around the courthouse, Mr. Lieberman, a quiet, cerebral man, is most often found sitting in silence beside his colleagues, taking notes on constitutional issues.

In his response, Mr. Lieberman began with an end run around the defense motion: He conceded that the grand jury had seen no evidence of hatred for gay men, but argued that Justice Konviser-Levine had approved the indictment, thus implicitly rejecting the same defense arguments.

In addition, he argued, if lawmakers had intended to make prosecutors prove defendants hated their victims, the Legislature would have said so in the law's final language.

''By contrast with New York State,'' Mr. Lieberman wrote, ''other states have hate crime statutes that require evidence of bias, animus or prejudice.''

Citing legal scholars, he suggested that hate crime prosecutions without evidence of hatred could benefit society. As in the era of racially motivated lynching, he noted, prosecutors could alter perceptions of vulnerability among certain groups and impunity among others.

At the hearing yesterday, friends and relatives of Mr. Sandy's sat opposite supporters of the defendants. All paid rapt attention as Justice Konviser-Levine probed the merits of the motion. In its intellectual exercise, the hearing departed from the usual tenor of the courthouse, a place more fertile for high dudgeon, emotional drama and accidental comedy.

In his oral argument, Mr. Lieberman said the hate crime law was meant to address a deep social problem.

Justice Konviser-Levine, who is due to rule in August, asked him whether he meant the law was ''nothing more than rhetoric?''

To the contrary, Mr. Lieberman argued, the law was valid and fit these defendants because ''they chose to go to a gay Web site, and there was a particular remark made by one of the defendants that this was an easy way to rob people.''

Then the defense lawyer, Mr. Di Chiara, split that point even more finely: ''The victim here was chosen because he was an easy target,'' he said, ''not because he was gay.''